Question

Which equation represents a line parallel to the line shown on the graph?

On a coordinate plane, a line goes through (negative 2, 0) and (0, 4).
A. y = one-half x - 2
B. y = negative one-half x + 3
C. y = 2x + 1
D. y = negative 2x + 4

Answer 1

To find a line parallel to the given line, we calculate the slope of the original line, which is 2. Lines that are parallel have the same slope, and thus the correct answer is option C, y = 2x + 1.

Step-by-step explanation:

The question asks which equation represents a line parallel to the given line on a graph. To determine which line is parallel, we need to find the slope of the given line. Using the points provided, (negative 2, 0) and (0, 4), we can calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). This results in a slope of (4 - 0) / (0 - (-2)) = 4 / 2 = 2.

For two lines to be parallel, they must have the same slope. Therefore, we are looking for an equation with a slope of 2. Option A has a slope of one-half, option B has a slope of negative one-half, option C has a slope of 2, and option D has a slope of negative 2. Only option C, y = 2x + 1, has the same slope as the given line, making it parallel to the given line.